Time Series Foundation Models (TSFMs) have achieved remarkable zero-shot performance through extensive pre-training on massive time series datasets. Nevertheless, due to the low-dimensional properties and diverse structural patterns of time series data, performing naive fine-tuning on TSFMs often leads to overfitting and falling into the mean-prediction trap. To address these challenges, we propose SIFT, a robust adaptation method that enhances time series foundation models by preserving Semantic Invariance and structural Fidelity throughout the fine-Tuning process. We employ semantic-invariant adversarial augmentation, which utilizes semantic spectrum decomposition to partition the semantic space and then generates perturbations within the non-core semantic subspace to bolster the model's robustness against these perturbations, mitigating overfitting. We implement a component-based structural fidelity enhancement, which facilitates component-wise mixup and imposes a reconstruction objective to improve the model's ability to preserve structural fidelity, alleviating the mean-prediction trap. Extensive experiments on representative TSFMs covering 10 real-world datasets demonstrate that SIFT can significantly enhance the performance of TSFMs.